There are elastic, and inelastic, demand curves. Normally, things purchased (like STEM labor) are never truly inelastic. The only inelastic example I can come up with would be a lifesaving medicine. If a medicine were 100% guaranteed to save your life, you would probably pay (almost any) economic cost. Even then, I don't think most people would pay ANY cost. This is also true over different time periods - gasoline may appear inelastic over the short term, but over the long term people make substitutions (public transit, electric vehicles, flex fuel...) to deal with rising costs.
Any 'shortage' or 'surplus' is ONLY AT A SPECIFIC PRICE POINT (and more specifically, also for a specific time period.) There are not ever really any such things are shortages or surpluses - just buyers and sellers that will not change their perspective on what something "should" cost. If there is a shortage, the price will go up until people stop wanting to buy. If there is a surplus, the price will go down until everything is bought or production is no longer profitable. No one ever talks about the surplus of worthless college degrees - the price employers pay for them simply goes down until it is equal to unskilled labor. The only reason these terms even exist in economics is because of externalities (governments restricting the input of some good, or the output of another.)
I took about a year of college economics. The fact that I constantly hear about shortages of things is crazy to me, jack the price (increase profit) and less buyers will be interested in purchasing. There will be no shortage. If there is a surplus, drop the price until there is no profit, then stop production. That takes care of the surplus.